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Full text of "Strain-Gage Loads Calibration Parametric Study"

IDtS §334 



24'" INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES 



STRAIN-GAGE LOADS CALIBRATION PARAMETRIC 

STUDY^ 

William A. Lokos*, Rick StauF* 
*NASA Dryden Flight Research Center, **Spiral Technology Inc. 

Keywords; calibration parametric study, loads calibration optimization, loads calibration test, 

loads test design, strain-gage calibration 



Abstract 

This paper documents a parametric study of 
various aircraft wing-load test features that 
affect the quality of the resultant derived shear, 
bending-moment, and torque strain-gage load 
equations. The effect of the following on derived 
strain-gage equation accuracy are compared: 
single-point loading compared with distributed 
loading, variation in applied test load 
magnitude, number of applied load cases, and 
wing-box-only compared with control-surface 
loading. 

The subject of this study is an extensive 
wing-load calibration test of the Active 
Aeroelastic Wing F/A-18 airplane. Selected 
subsets of the available test data were used to 
derive load equations using the linear 
regression method. Results show the benefit of 
distributed loading and the diminishing-return 
benefits of test load magnitudes and number of 
load cases. The use of independent check cases 
as a quality metric for the derived load 
equations is shown to overcome blind 
extrapolating beyond the load data used to 
derive the load equations. 



1 Introduction 

Structural load measurement obtained from 
aircraft in flight has been depended upon for 
many decades for research and safety-of-flight. 
This measurement involves the installation 
of strain gages on the primary load paths and the 

This work was prepared as part of the author's official 
duties as an employee of the U. S. Government and in 
accordance with 17 U.S.C. 105, is not available for 
copyright protection in the United States. NASA is the 
owner of any foreign copyright that can be asserted for 
the work. 



2. 



3. 



calibration of these sensors through the 
application of known loads. Load equations are 
derived from the post-test analysis of these 
recorded applied loads and the strain-gage 
output data [1]. These load equations are then 
used to interpret subsequent strain-gage outputs 
when the applied loads are not otherwise 
known— such as in flight. The accuracy of these 
load-equation-calculated flight loads is subject 
to many variables, the bulk of which can be 
grouped into three categories: 
1. the design of the strain-gage installation, 

the design and performance of the 

applied-load test, and 

the strain-gage load equation derivation 

process. 
The focus of this paper is the design of the 
applied-load test. The three major questions to 
be answered are: 

1. Which features of a strain-gage calibration 
load test have a significant relationship 
with the accuracy of the resultant load 
equations? Designers of such tests need an 
understanding of the relative merit of the 
various testing options in order to design a 
test that will produce the required quality 
of output while considering schedule time 
and cost constraints and avoiding 
subjecting the airframe to unnecessary 
risk of damage. 

2. If testing the structure to a higher applied 
load is better than testing to a lesser 
load— how much load will suffice? 

3. If a greater number of independent 
applied-load cases is better than fewer 
cases— how many load cases will suffice? 

This research effort addresses these and similar 
questions. 



LOKOS, STAUF 



The origin of the database for these 
parametric studies is the strain-gage load 
calibration test of the Active Aeroelastic Wing 
[AAW] F/A-18 aircraft, performed at the NASA 
Dryden Flight Research Center Flight Loads 
Laboratory [2] in 2001. The AAW aircraft, 
shown in figure 1 , is the test bed for the AAW 
project [3, 4], which seeks to explore the use of 
wing elastic twist for roll control. The primary 
structure and flight control system of the aircraft 
were modified for that goal, and the structure 
heavily instrumented. Because the AAW project 
requires full exploitation of wing strength, many 
strain gages were placed on the wing structure 
to support real-time monitoring of component 
loads relative to strength limits. The load 
calibration test [5] used to calibrate these gages 
was intentionally more elaborate than necessary 
for the basic calibration and was designed to 
provide a broad database for parametric study. 

2 Nomenclature 

AAW Active Aeroelastic Wing 

check-case 



CKCS 

DLL 

EQDE 

NASA 

rms 
TLL 

3 Analysis 



design limit load 

EQuation DErivation; in-house 
linear regression analysis package 

National Aeronautics and Space 
Administration 

root mean square 

test limit load 



3.1 Strain-Gage Instrumentation 

The analysis method used here is determined 
by the instrumentation available on the AAW 
test aircraft. Figure 2 shows the location of 
the 20 component load measurement reference 



stations. The research reported here only 
examines the right-wing-root shear, bending 
moment, and torque; and the right-wing-fold 
shear, bending moment, and torque. Figure 3 
shows the locations of the strain-gage 
instrumentation on the aircraft structure. 
Each strain-gage bridge is configured as a 
four-active-arm Wheatstone bridge. The wing 
structure includes seven spars in the inboard 
wing and six spars in the outboard wing. The 
wing design has a low aspect ratio and has 
highly redundant load paths. Additionally, a 
wing fold interrupts the spanwise load paths. 
These features make the F/A-18 wing a 
challenging structure for the derivation of good 
load equations. The wing-box strain-gage 
bridges were installed on the wing-root attach 
lugs, the wing skin, and on the webs of some of 
the spars as well as the wing-shear ties. Much of 
the strain-gage installation design here follows 
the pattern of previous F/A-18 loads aircraft 
practice. The 32 strain-gage bridges at wing 
station 65, however, were added specifically 
for strain-gage calibration research. A total of 
158 strain-gage bridges were present on the left 
and right wing boxes. 

3.2 Load Tests 

The analysis method is also determined by the 
ground-loading test approach. Figure 4 shows 
the 16 load zones for the left wing. Each load 
zone was served by one load column comprised 
of a hydraulic cylinder, a load cell to measure 
the applied load, and a whiffletree mechanism 
to distribute the load to two, three, or four load 
pads. A total of 104 load pads were bonded to 
the lower surface of the wings to allow both 
tension and compression loading. These pads 
covered approximately 60 percent of the lower 
wing surface. Left and right wing loads were 
mirror images of each other, and the aircraft was 
always symmetrically loaded. A wide range of 
single-point- (one load zone per wing), 
double -point- (two load zones per wing), and 
distributed-load (16 load zones per wing) cases 
were performed. The total number of load cases 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



was 72. The maximum net vertical load 
exceeded four times the gross weight of the 
aircraft during distributed loading. Figure 5 
shows the aircraft in ground test undergoing 
a distributed-load case. All load zones are 
active in this photo. Figure 6 shows a typical 
single-point load application. In this photo, load 
zone 16 is active while all the other load 
columns are disconnected. The bonded-on load 
pads and whiffletrees produced a tare weight 
effect because of their structural deadweight. 
This effect was transparent to the calibration 
process, as it was a constant force throughout 
each load run. Figures 7a and 7b show the 
wing-root bending moment and torque envelope 
with the single-point and distributed applied test 
loads. In these figures the notations SI and Dl 
refer, respectively, to the single-point and 
distributed-load cases. The maximum test loads 
went to about 70 percent of flight design limit 
load [DLL] for the distributed loading. 
Figure 7a shows the small amount of the load 
envelope exercised by the single-point loading. 
Load cells were carefully calibrated and 
applied-load data and strain-gage data were 
recorded with 14-bit resolution. The actual 
load pad and hydraulic jack locations were 
determined using a three-head- sending theodolite 
measurement system. These processes provided 
for determining applied loads and moments with 
excellent precision. Reference 5 gives further 
details. 

3.3 Load Equation Derivation 

Strain-gage load equations were derived from 
selected subsets of the available recorded test 
data using an in-house linear regression analysis 
package called EQuation DErivation, or EQDE. 
Utilizing a modern desktop computer, EQDE 
derives the coefficients for user- selected 
combinations of strain-gage bridges based on 
analysis of the user-input test data. These test 
data consist of recorded measured applied loads 
and the corresponding strain-gage outputs. 
EQDE also automatically derives load equations 
for all possible strain-gage combinations from 
the input data. For example, if the user inputs 



test data from 20 strain-gage bridges, the 
software can be used to generate load equations 
for all possible combinations of two, three, four, 
and five strain-gage bridges. This thorough 
approach is termed an "exhaustive search" and 
is possible because of the computing speed of 
modern computers. No longer does the user 
need to judiciously select a limited number of 
strain-gage combinations as recommended in 
reference 1. It is always prudent, however, for 
the user to understand the reasonableness of the 
product of any software. 

3.4 Load Equation Evaluation 

EQDE also computes the root mean square 
[rms] of the fit of the derived load equation to 
the test data from which it was derived. This 
EQDE rms evaluation provides a quantitative 
metric indicating how well the derived 
equations represent the test data used in their 
derivation. EQDE ranks the order of derived 
load equations based on this computed rms so 
that the user need only consider the best of 
perhaps thousands of prepared equations. 
This research effort uses the EQDE rms as one 
metric of load equation quality. Of the 72 total 
load cases, 24 were fully distributed, utilizing 
32 load zones simultaneously. Four of these 
distributed-load cases were set aside for use as 
an independent check case for the derived 
equations. These four load cases were excluded 
from use in the load equation derivation 
process. Figure 7c shows the four check-load 
cases, which are diverse, flight-like, 
independent-load cases. For each load equation 
studied, the rms fit of the load equation to these 
four load cases was calculated. This check-case 
rms computation is used as the second metric of 
equation quality. This second metric indicates 
how well the derived load equations can 
calculate loads for load cases from which they 
were not derived. This check-case rms therefore 
provides some additional insight into how well 
the load equations will perform with flight data. 
By deriving load equations from selected load 
cases, or parts of load cases, and then studying 
the resultant EQDE and check-case rms values. 



LOKOS, STAUF 



one may observe the relative benefit of 
designing a load calibration test using only 
those load cases. 

EQDE equation rms error = 



2 (Derived load,- - Measured load ,■ ) 

t=l 



(1) 



2 (Measured load ,■ ) 

t=l 



Check-case equation rms error = 



2 (Derived load,- -Check load,V 

t=l 



(2) 



2 (Check load,) 
t=l 



Figure 7d shows a graphical comparison 
of the measured applied test loads of 
distributed-load case B against outputs of two 
wing-root bending-moment equations, one 
derived from single -point loads and one derived 
from distributed loads. The outputs of each load 
equation were calculated using the strain-gage 
outputs that were recorded as these measured 
test loads were applied. The applied load curve 
is used as the truth model. If a load equation 
produces a line that closely fits the applied load 
curve, the indication is that this equation 
performs well in this part of the test load 
envelope. For a further comparison, the load 
equation outputs can be calculated and 
compared graphically against each of the four 
independent check cases. An equation that 
closely fits all four check cases can be expected 
to perform well throughout the entire flight 
envelope. The graphical comparison of a load 
equation with all four check cases can be 
replaced by a single numerical value when the 
rms of the differences is calculated. This is the 
check-case equation error defined above. 
Jenkins and Kuhl recognized the need for 
independent evaluation of derived load 
equations [6]. 



4 Results 



4.1 Strain-Gage Location and Behavior 
Considerations 

Figure 8 illustrates two types of strain-gage 
response to test load. The outputs of a wing-lug 
bridge and a nearby skin bridge are plotted 
against the applied load from a single-point load 
case on zone 7. The lug bridge has a very 
nonlinear response, while the skin bridge 
demonstrates linear behavior. If paired with 
another lug bridge that has a similar 
but opposite trend, the nonlinear lug bridge can 
still be useful. While both bridges can 
be effectively used in load equations, the 
lug-bridge representation is expected to suffer at 
low applied loads while the skin-bridge 
response can be readily captured even at 
relatively low applied test load. While this does 
demonstrate the broad variation possible 
amongst diverse instrumentation, the following 
trends are presented for potential application to 
the design of future load calibration tests. 

4.2 Data-Conditioning Techniques 

Test data used in these various parametric 
studies were filtered for noise spikes. In each 
case one increasing- and one decreasing-load 
test data segment was used. In some cases, 
data produced above a specified load level 
were excluded from the derivation input 
as noted, but even then the increasing- and 
decreasing-load data segments were both used. 
Data-conditioning was applied as uniformly as 
possible throughout so as not to introduce an 
artificial variation where one did not already 
exist. 

4.3 Single-Point Compared With Distributed 
Loading 

Figure 9a shows a comparison of the best two-, 
three-, four-, and five-gage wing-root-shear, 
bending-moment, and torque equations derived 
from single-point loading and from distributed 
loading. The check-case rms error for each 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



equation is plotted against its EQDE rms error. 
The most desirable area of the plot is low and 
left. A first observation is that allowing the 
inclusion of more gages generally improves the 
EQDE rms error and the check-case rms error. 
Figure 9b shows the same comparison but only 
for the four-gage equation results. This allows a 
less -cluttered comparison. The trend here is for 
the equations derived from distributed-loading 
test data to be better than those derived from 
the single -point loading test data. Figure 10 
shows the same trend for wing-fold load 
equations. The better results produced by the 
distributed-loading database are the result of 
two merged features. While the obvious 
difference is that the distributed-loading cases 
involved all 16 load zones simultaneously as 
opposed to the one-zone-at-a-time process of 
the single-point loading, the distributed-loading 
cases produced much higher total net load 
than did the single-point loading cases. Figures 
7a and 7b show the maximum net test load 
comparison between the single-point and 
distributed-load cases performed for this study. 
This emphasizes a typical limiting factor of 
single -point loading. When loads are introduced 
to the test structure through surface-contact load 
pads there is often a surface peak pressure 
limit, as required by local skin-bending or 
substructure-crushing considerations. Under 
these circumstances, the distributed-loading 
approach offers more total surface area than 
single-point loading can achieve. It is not 
possible to simply use a single huge load pad 
because of the high peak-to-average pressure 
ratio that would be produced by the combination 
of an elastic load pad in contact with an elastic 
wing. Similarly, there are practical limitations to 
the number of load pads one might want to 
accommodate. While the comparisons shown in 
figures 9 and 10 do not indicate the relative 
merit of these two features (load distribution 
and total load magnitude), they do clearly 
indicate the superior results produced by the net 
effect of the distributed-loading approach 
over the single-point loading scheme. It should 
be noted that reference 7 gives an example of a 
B-1 wing that was calibrated using both a 



distributed-load approach and a single -point 
load approach and concluded that there was 
very little difference in loads calculated from 
the two methods. The difference in the test load 
magnitude between single-point loading and 
distributed-loading, as indicated in figures 7a 
and 7b, is considered significant. 

4.4 Test Load Magnitude Effect 

This section presents the effect of varying the 
maximum applied load. Figure 11 shows the 
EQDE and check-case rms errors plotted against 
applied test load for four separate four-bridge 
wing-root bending-moment equations derived 
from the 16 single -point load cases. The effect 
of varying the peak magnitude of the applied 
test load was produced by selecting appropriate 
segments of the available load test data as input 
to EQDE. Separate load equations were derived 
for each increment of load, that is, 25, 50, 75, 
and 100 percent. Figures 12a and 12b 
graphically describe this approach. The 16 
single-point load and strain-gage data sets were 
truncated at 25, 50, and 75 percent and used in 
addition to the full -range test data to vary the 
peak load magnitude. Wing-root bending 
moment was chosen from the six component 
loads to illustrate this trend. Wing-root bending 
moment is representative of the general trend of 
all data. Figure 1 1 shows a steady trend of 
slight improvement in the EQDE rms error for 
increasing load. With regard to check-case rms 
error, the same trend direction can be seen. This 
trend is not nearly as uniform, but shows a 
greater overall effect. One likely reason for the 
erratic check-case rms error trend is the 
considerable disparity in net applied test load 
magnitude between the single -point load cases 
and the distributed-load cases. This disparity is 
especially large when the single -point test data 
is truncated, as in this example. Remember 
that the check cases are a family of four 
distributed-load cases that reach 70 percent 
of the aircraft DLL. The extrapolation ratio 
involved in the use of load equations derived, 
from single-point test loading data truncated to 
25 percent, to calculate these check-case loads is 



LOKOS, STAUF 



about 10:1. If these equations were used with 
full-envelope flight data, the extrapolation ratio 
would be greater than 14:1. Another matter to 
keep in mind when considering the use of very 
small applied test loads is the presence of 
nonlinear gage responses, as shown in figure 8. 
The comparisons of the wing-fold-station 
bending-moment equations, which did not 
employ lug-mounted gages, were more linear. 

Figure 13 shows the variation of the 
EQDE and check-case rms errors plotted against 
applied test load for four-gage wing-root 
bending-moment equations derived from 19 
distributed-load cases. Here again, the effect of 
varying the magnitude of the maximum applied 
test load was produced by step-wise progressive 
truncation of the test data prior to equation 
derivation. This comparison, as with the 
single-point loading, shows a clear trend of 
improving EQDE rms error as applied test load 
is increased. This occurs in the check-case rms 
curves as well. The general improvement in 
accuracy is a factor of about two and one-half as 
the applied load increases by a factor of four. 
Although we are still concerned with nonlinear 
lug-mounted gages, the trends here show 
smaller nonlinearities than those produced by 
the single -point loading data. This is attributed 
to the greater overall applied loads produced 
by these distributed-load cases. The trends 
here indicate the diminishing benefit of the 
increasing applied load above 50 percent of 
applied test load. The EQDE rms error and the 
check-case rms error do not change linearly 
with the change in applied test load. While it 
has generally been thought that the best way to 
calibrate strain gages is to apply test loads 
equal to the maximum expected flight loads, 
here it can be understood that much of the 
benefit can be achieved by applying about 
half (75 percent DLL x 70 percent DLL) of 
the expected flight load. This obviously is 
influenced by the nonlinear nature of the 
structure-strain-gage installation combination. 
If one is able to assess the linearity of a planned 
test article relative to the F/A-18 wing used 



here, then one may consider this finding useful 
in designing loading for a calibration test. 



4.5 Effect of Number of Load Cases 

In order to examine the effect of the number of 
load cases on the quality of the derived load 
equations, a series of EQDE runs were made. 
The first run utilized the test data from all 
16 single-point load cases as input. All of the 
load cases in this study went to 100 percent of 
test limit load [TLL] (represented in figure 7a). 
The second run utilized the data from only 15 of 
these test cases. Each subsequent derivation run 
dropped off one more load case data set until 
only the minimum number of cases was used. 
EQDE requires that there be equal or more 
load cases than the number of strain gages 
present in the derived load equations. The 
rms errors for the best four-gage wing-root 
bending-moment equations (based on the EQDE 
rms error values) that were produced from this 
study are reported in figure 14, plotted in order 
of increasing number of load cases. Table 1 
shows the load case drop list. The order of this 
list was selected based on engineering judgment 
with the goal of gradually thinning the database. 
These load cases correspond to the load zones 
shown in figure 4 and the envelope loads shown 
in figure 7a. Figure 14 shows two general 
trends. As the number of included test cases is 
reduced the EQDE rms error trends downward, 
while the check-case curve eventually shows 
improvement in rms error magnitude. While 
the shapes of these curves are somewhat 
path-dependent— that is, they are related to the 
order in which the individual load cases were 
omitted— the trend shown here is that for 
this test- and load-case drop order, the most 
acceptable load equations were derived from 13 
or more load cases. Please note that in the 
context of these low net load single -point load 
cases, the larger net load distributed-check-case 
rms errors are a stronger indicator of practical 
quality. 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



Table 1 . Single-point load case attrition list. 



Table 2. Distribution-load case attrition list. 



Drop set 
number 


Load case 
number 


1 


S16 


2 


S15 


3 


S14 


4 


S2 


5 


S12 


6 


S7 


7 


S8 


8 


Sll 


9 


S13 


10 


S4 



The same study of the effect of varying 
the number of load case data sets was performed 
within the context of distributed-loading tests. 
Figure 15 shows the EQDE rms and the 
check-case rms error curves for increasing 
numbers of distributed-loading cases. Table 2 
shows the load case drop list; the load case 
envelope plot is given in figure 7b. Here again, 
the trend is that the EQDE rms error curve 
moves upward overall while the check-case rms 
error curve trends downward. The load 
equations that were used by the AAW project 
for safety-of-flight and research were generally 
derived using all available distributed-load 
case data. While, again, this is somewhat 
configuration-dependent, it is obvious that 
satisfactory load equations could be derived 
using anywhere from 6 to 19 diverse load cases. 
In fact, no significant benefit is indicated for the 
additional distributed-load cases beyond the 
minimum six used here. For this test, only 
six distributed-load cases produced results 
slightly better than the results produced by 
13 single -point load cases. This is largely a 
function of the greater net load of the 
distributed-load cases. With regard to figure 15, 
the EQDE rms errors and the check-case rms 
errors carry equal credibility as they both are 
based on high-load data. 



Drop set 
number 


Load case 
number 


1 


D3 


2 


D20 


3 


D16 


4 


D22 


5 


D15 


6 


D21 


7 


D4 


8 


DIO 


9 


D17 


10 


D23 


11 


D6 


12 


D12 


13 


D18 


14 


Dl 



4.6 Wing Surface Availability Effects 

While it is most desirable to widely distribute 
the applied test loads at least in the aggregate if 
not in each load case, sometimes there are 
practical considerations that interfere with this. 
Surface-mounted instrumentation, imbedded 
sensors, or other fragile skin features may not 
permit contact pressures in the range of 20, 30, 
or higher psi as would otherwise be desired. 
Reference 7 includes a discussion of these types 
of restrictions in the load calibration of a B-2 
wing. This section will address the effects on 
load equation rms errors of loading only the 
control surfaces or only the wing box. These 
issues were studied by segregating subsets of 
the single- and double-zone load test data sets 
and deriving load equations for each group of 
test data. Figure 16 shows a comparison of six 
sets of wing-root-shear load equations. The plot 
format is check-case rms error plotted against 
EQDE rms error with the best quality being low 
and left. The six load case sets are: 



LOKOS, STAUF 



single-zone loading on all wing zones 

(baseline), 

single-zone loading on the control 

surfaces only, 

single- and double-zone loading on the 

control surfaces only, 

single-zone loading on the wing box 

only, 

single- and dual-zone loading on the 

wing box only, and 

single- and dual-zone loading on the 

entire wing. 

An observation is that there is some 
benefit produced with regard to check-case 
rms error by adding some dual-load cases, 
especially in the "wing-box-only" situation. It 
is interesting to note that it was possible to 
produce shear equations of similar quality to the 
baseline of "all single-point cases" using 
"control- surfaces single-point cases only" or 
"wing-box single- and dual-point cases." 

Figure 17 shows wing-root bending-moment 
equation results derived from the same 
segregated test data sets. Here, the benefit of 
including dual-zoneloading cases is very evident 
between the two "control- surface-only" sets. 
Although this same benefit is not as evident 
between the two "wing-box-only" sets, they are 
at no disadvantage compared with the two 
"all-wing" sets. As with the shear equations 
example, it is noted that bending-moment 
equations of roughly equivalent quality can be 
produced using less than the baseline of "all 
single-point cases." 

Figure 18 shows the wing-root-torque 
equation results derived from the same 
segregated test data sets. Here, it is obvious that 
giving up the greater torque-arm length of the 
control surfaces is a big disadvantage as shown 
in the two "wing-box-only" sets. Both of the 
"control-surfaces-only" groups returned good 
results. This emphasizes the importance of 
control- surface loading to the generation of 
good wing-root-torque equations. 



5 Summary and Conclusions 

Various issues regarding the design of aircraft 
strain-gage calibration loading tests have been 
discussed in this paper including: single-point 
loading compared with distributed loading, test 
load magnitude, number of load cases, and wing 
surface availability for loading. The importance 
of understanding the linearity of the strain-gage 
location has been emphasized, as well as the 
importance of using independent flight-like load 
cases for interpreting equation quality. Within 
the scope of this research effort it has been 
concluded that the distributed-loading approach 
generally yields superior results when compared 
with those produced by the single-point loading 
approach. This effect has been shown to be a 
result of the much greater net load magnitude 
possible with the distributed-loading approach. 
The effect of load magnitude was studied 
separately and found to be significant, however, 
while this test applied a peak of 70 percent 
design limit load, it was found that similar 
results could have been produced at only 
50 percent design limit load. Although the load 
equations selected for use in safety-of-flight and 
flight research were derived from two dozen 
distributed-load cases, this study has shown that 
satisfactory equations could have been derived 
using as few as six diverse distributed-load 
cases. It has been found that when dealing with 
the matter of some structure being off-limits to 
loads testing, wing-root-torque equation quality 
depends heavily on control-surface loading. 
Wing-root- shear equation quality sometimes 
improves with the addition of some dual-point 
load cases. It was further suggested that greater 
improvements might be produced if all available 
load zones were used to produce some large 
distributed-load cases. Wing-root bending-moment 
equation quality was maintained through either 
wing-box-only loading or control-surface-only 
loading. The use of a set of independent, 
diverse, flight-like distributed loads to check the 
quality of the derived load equations was found 
to be a valuable asset. 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



References 

[1] Skopinski T H, Aiken W S Jr and Huston W B. 
Calibration of strain-gage installations in aircraft 
structures for the measurement of flight loads. 
NACA Report 1178, 1954. 

[2] Dryden Flight Research Center, Flight loads 
laboratory. Last modified September 24, 2001. 
http://www.dfrc .nasagov/Research/Padlities/FLL/index.html 
Accessed April 8, 2004. 

[3] Pendleton E, Griffin K E, Kehoe M W and Perry B. 
A flight research program for active aeroelastic wing 
technology. AIAA 96-1574. 1996. 

[4] Pendleton E, Bessette D, Field P, Miller G and 
Griffin K. Active aeroelastic wing flight research 
program: technical program and model analytical 
development. Journal of Aircraft, Vol. 37, No. 4, pp. 
554-561, 2000. 

[5] Lokos W A, Olney C D, Chen T, Crawford N D, 
Stauf R, and Reichenbach E Y. Strain gage loads 
calibration testing of the active aeroelastic wing 
FIA-18 aircraft. NASA/TM-2002-2 10726, 2002. 

[6] Jenkins J M and Kuhl A E. A study of the effect of 
radical load distributions on calibrated strain gage 
load equations. NASA TM 56047, 1977. 

[7] Jenkins J M and DeAngelis V M. A summary of 
numerous strain-gage load calibrations on aircraft 
wings and tails in a technology format. NASA 
Technical Memorandum 4804, 1997. 



LOKOS, STAUF 



Figures 




EC02-0264-16 



Fig. 1 . AAW aircraft in flight. 




Trailing edge flap / 
hiinge moment — 



Aileron hinge moment 



Wing root shear, bending moment, and torque 
-Inboard leading edge flap hinge moment 
- Wing fold shear, bending moment, and torque 
Outboard leading edge flap hinge moment 



Fig. 2. Component load locations. 



10 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



^ Shear gages 

n Bending gages 

o Torque gages 

o Lug or transmission gages 




Fig. 3. Strain-gage bridge locations. 



Inboard 
leading 
edge flap 



r— Wing 
\ root load 
\ reference 
/-p. location 

FS 475.00 in. 
BL ±38.50 in. 



Trailing 
edge flap 



Wing fold load 
reference location 
FS 514.90 in. 
BL ±162.50 in. 




Outboard 
leading 
edge flap 



Aileron 



Fig. 4. Loading zones. 



11 



LOKOS, STAUF 




ECO 1-0249-06 

Fig. 5. Composite photograpli of AAW aircraft undergoing distributed loading at zero load and at maximum up load. 




ECO 1-0249-52 

Fig. 6. AAW aircraft in single-point loading (zone 16); right wing shown. 



12 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 

































/" 












"^ 


y — ' est limit oad 






/ 


/ 














\ 


V 








< 






S6 


S8 <i5 S3 








\ 


s. 




E 
o 
E 


\ 


\ 




S4 
S2 « 


N^^ 


A 


S1 

/ 








\ 




■a 
c 

0) 

^ 

e 

CD 

C 




\ 






^ 




^ 


.^ . 






\ 








\ 


S9 


---^ 






,4 . 


/ 




y'i 


f^ 


^^^ 


— -s 


^ 






\ 


^ 


S10 




S11 ^12 S6 J 


/ 
















^ 








/ 



































Wing-root torque, in-lbs 
(a) Root bending-torque single-point load cases. 




Wing-root torque, in-ibs 

(b) Root bending-torque distributed-load cases. 

Fig. 7. Load envelopes. 



13 



LOKOS, STAUF 





Distrib 


jted case 


B 










/ 


- Test Mr 


lit load 










>- 


fv 










^-^ 


s. 


1 

. Disti ibuted case C 

/ 1 


in 


/ 


/ 


\ 












N 


/ 






c 
c 

0) 

E 
o 
E 

G) 

C 


< 














y^ ' 


-5' 


\ 


s. 




\ 


\ 










. 








\ 




T3 

C 
0) 

SI 

■c 




\ 


















\ 




o 

CD 

c 






\ 






.--^ 








y 


/ 






Distr 


buted ca 


,.> 










% 


> 


/ 


















^__ 






/^ 


























Distri 


}uted cas 


eD 





Wing-root torque, in-lbs 

(c) Root bending-torque check-case distributed-load cases. 
Fig. 7. Continued. 



14 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



105 
100 
95 
90 
85 
80 
75 
70 
^ 65 

0) 

^ 60 
55 



0) 

a. 



2 50 



B 45 



o 

0) 
0. 



40 
35 
30 
25 
20 
15 
10 



Applied load: check case B 
Equation from single-point loading 
Equation from distributed loading 






50 



100 



150 



200 



250 
Time, sec 



300 



350 



400 



450 



500 

040104 



(d) AAW derived wing-root bending equations compared witli applied load. 

Fig. 7. Concluded. 



15 



LOKOS, STAUF 



-.20 



Upper wing root aft lug bridge 
Upper wing forward torsion bridge 




-3000 



-2000 



-1000 1000 

Applied load, lbs 



2000 



3000 



Fig. 8. Bridge output compared with load for a lug bridge and a skin bridge. 



16 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



10 



u 



O Two-gage equation 

□ Three-gage equation 

A Four-gage equation 

O Five-gage equation 



Shear equation from single point 

Shear equation from distributed 

Bending equation from single point 

Bending equation from distributed 

Torque equation from single point 

— — Torque equation from distributed 





9 . 


:) 
















/ 
/ 






K 














/ ; 






-^___ 












i / ^ 










--~.__^ 


-- .^__ 


■P) 




>J ■ 
















1 


P 
















n 


1 

.0 


Dir 
impro 


iction of 
ring quality 
































^ 
















^ 



















10 15 20 25 30 

EQDE equation rms error, percent 



35 



40 



45 



(a) Error comparison of best two-, three-, four-, and five-gage wing-root load equations derived from 
single-point and distributed-Ioading tests. 

Fig. 9. Error comparisons. 



17 



LOKOS, STAUF 



10 



q 

3 

0) 
0) 
tf) 



O 



O Four-gage shear equation from single point 
# Four-gage shear equation from distributed 
D Four-gage bending equation from single point 
■ Four-gage bending equation from distributed 
A Four-gage torque equation from single point 
; torque equation from distributed 



A Four-gage i 



























o 
















































i 




















A 
















€ 


















■ 























































10 15 20 25 30 

EQDE equation rms error, percent 



35 



40 45 

040107 



(b) Error comparison of best four-gage wing-root load equations derived from single-point and 
distributed-loading tests. 

Fig. 9. Concluded. 



18 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



18 



16 



14 



u 10 



:: 8 

o 
o 



E 

DC 



O Four-gage shear equation from single point 
# Four-gage shear equation from distributed 
D Four-gage bending equation from single point 
■ Four-gage bending equation from distributed 
^ Four-gage torque equation from single point 
A Four-gage torque equation from distributed 







A 
















A 






























c 


> 




























































[ 


'• A 














■ 

















6 8 10 

EQDE equation rms error, percent 



12 



14 



16 



Fig. 10. Error comparison of wing-fold load equations derived from single-point and distributed-loading tests. 



19 



LOKOS, STAUF 



—A— Four-gage equation EQDE rms error 
—A- Four-gage equation CKCS rms error 



18 














































16 














































c 14 

0) 














































o 
















































a. 










> 


\ 












2 1? 










y 
y 

^ 


\ 
\ 












0) 










y 


\ 












VI 










y 


\ 
\ 












E 








y 

/> 














c 
o 








y 




\ 
\ 












13 10 














































3 












\ 












<U 

CO 






K 






' 


\ 










o 














\ 










g 8 














\ 






















\ 










■D 














\ 










10 














\ 










LIJ 














\ 










Q 
2 6 














\ 












































^ 


\ 


























N ^^ 






\. 


















\ 
























\ 








4 






































\ 
























^-. 














— n 


\ 


2 















































10 20 30 40 50 60 70 80 

lUlaximum applied test load, percent of zone limit 



90 100 



Fig. 1 1 . Effect of variation of maximum test load on wing-root bending-moment equation errors (derived 
from single-point loading tests). 



20 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



100 



80 



60 



40 



^ 20 

c 
a> 
o 

^ 

a. 

'^ 
o 

■D 

a. 
a. 
< -20 



-40 



-60 



-80 



-100 



r 


V 


Percent of 






/ 


\ 












applied 
load 






/ 


\ 












lUO 






/ 
/ 














75 
50 
25 




1 




\ 
















1 






\ 














1 




















1 






\ 














1 






V 














• 
• 






• 
* 












* 
• 
• 


• 
« 

• 

• 

• 






• 
• 
• 
• 
• 
• 
• 
• 
• 






















• 
* 
• 
• 
• 
« 
• 
• 
• 
• 






4 

• 
• 
* 
• 
• 
• 


• 
* 












• 






* 














\ 






/ 














\ 






/ 














\ 






/ 














\ 


\ 

\ 


/ 


/ 
















\ 


/ 


















\ 


/ 


















\ 

\ 


/ 


















\ 


./ 







100 200 300 400 500 600 

Time, sec 



700 



800 



900 1000 

040110 



(a) AAW single-point load profile with percent load breaks. 
Fig. 12. Load profiles. 



21 



LOKOS, STAUF 



u 

a. 



■a 

0) 



100 



90 



80 



70 



60 



50 



a. 
a. 
< 40 



30 



20 



10 





1 \ Percent of 










/ 


\ 








applied 










/ 


\ 








load 










/ 


\ 






^^—^ 


75 










/ 


\ 


< 




^■^■^ 


50 
25 










1 
1 


/ 




\ 

\ 














1 






\ 














1 






\ 














1 






\ 














1 






\ 














1 
1 






\ 


L 












1 








\ 












1 








\ 












f 








\ 










> 










\ 










/ 










\ 










/ 










\ 










/ 










\ 










/ 










' 


k 








/ 












\ 






1 

* 


/ 

• 
• 












• 
« 
• 
• 
• 






• 
• 
• 
* 
• 
• 
• 
• 
• 
• 














• 
• 
• 
• 
• 
• 
• 
• 
• 
« 






• 
* 
• 
• 
• 
• 
m 














• 


• 
• 
• 
• 














N. 



50 



100 



150 



200 



250 
Time, sec 



300 



350 



400 



450 



500 



(b) AAW distributed-load profile with percent load breaks. 
Fig. 12. Concluded. 



22 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



—A— Four-gage equation EQDE rms error 
—A- Four-gage equation CKCS rms error 



10 



S 7 
u 

0) 

a. 
o 
% 6 



c 
o 



3 

a> 
CO 

o 

^ 4 

o 

■D 

c 

(0 
lU 

O 3 

LIJ 

































































































































As 
A 




s 


























> 


s 




N 


K 




























N 
S 

1 


k 


^ 


\ 


^N^ 


























"^ -^ 


--^ 







^^ 


1 


i 































































10 15 20 25 30 35 40 45 50 55 60 
Maximum applied test load, percent of flight limit load 



65 70 



75 



Fig. 13. Effect of variation of maximum test load on wing-root bending-moment equation errors (derived from 
distributed-loading tests). 



23 



LOKOS, STAUF 



18 



16 



—A— Four-gage equation EQDE rms error 
—A- Four-gage equation CKCS rms error 



14 



A- 



.-4 



c 
u 
(i) 
"^12 



0) 
V) 

E 
.1 10 

3 

a> 
tn 
o 

^ 8 

c 

10 
lU 
Q 
O 
UJ 



4 



A- 



X: A- 



.--'A 




10 11 12 

Number of load cases 



16 

040113 



Fig. 14. Effect of number of single-point load cases used on wing-root bending-moment equation errors. 



24 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



—A— Four-gage equation EQDE rms error 
—A- Four-gage equation CKCS rms error 



5.0 



4.5 



4.0 



a 3.5 
o 

0) 

a. 



4) 

to 

E 

c 
.9 

3 

o- 

0) 

u 
o 

■o 
c 

(0 
LIJ 
Q 

o 

LIJ 



3.0 



2.5 



2.0 



1.5 



1.0 



.5 















































-A 




r\ 








A--->_ A^--^ 


\ 


r^A.. 


i 




r^ 


I A 






'i 


r^i 


y-^—i 


i— A— i 


s— A 




r 























































10 12 14 

Number of load cases 



16 



18 20 

040114 



Figure 15. Effect of number of distributed-load cases used on wing-root bending-moment equation errors. 



25 



LOKOS, STAUF 



30 



25 



g 20 
o 

a. 



15 



3 



10 



O All single-point cases-baseline 

9 All single- and dual-point cases 

□ Control surfaces single-point cases 

H Control surfaces single- and dual-point cases 

A Wing box single-point cases 

A Wing box single- and dual-point cases 











































A 




































A 


O 

D 
• 1 


1 





























10 15 20 25 30 

EQDE equation rms error, percent 



35 



40 



45 

040115 



Figure 16. Effect of load zone availability and single- and double-zone loading on wing-root-shear rms errors. 



26 



STRAIN GAGE LOAD CALIBRATION PARAMETRIC STUDY 



14 



12 



10 



0) 

u 

Q. 



E 

c 
o 

o- 

0) 



All single-point cases-baseline 
% All single- and dual-point oases 

□ Control surfaces single-point cases 

1 Control surfaces single- and dual-point cases 
^ Wing box single-point cases 

A Wing box single- and dual-point cases 






4 6 8 

EQDE equation rms error, percent 



10 



12 

040116 



Figure 17. Effect of load zone availability and single- and double-zone loading on wing-root 
bending-moment rms errors. 



27 



LOKOS, STAUF 



30 



25 



S 20 
u 

0) 

Q. 



U) 

E 
I 15 

3 

o- 

0) 

a> 

U) 
(0 

o 

o 
o 

O 10 



All single-point cases-baseline 
% All single- and dual-point cases 

□ Control surfaces single-point cases 

1 Control surfaces single- and dual-point cases 
^ Wing box single-point cases 

A Wing box single- and dual-point cases 



A 










▲ 
































Ci* 










*^ 









10 15 

EQDE equation rms error, percent 



20 



25 



Figure 18. Effect of load zone availability and single- and double-zone loading on wing-root-torque mis errors. 



28